1. OPSM 301 Operations Management Class 21: Inventory Management: the newsvendor Koç University Zeynep Aksin zaksin@ku.edu.tr

2. Announcements  Quiz 5 on Thursday  Study: Location and transportation  Use questions at the end of the chapter to practice  Midterm 2 next Tuesday on 20/12 at 17:00 CAS-Z08  Exam does not include MT1 topics  Will have a review the same day in class

3. Single Period Inventory Control  Examples: –Style goods –Perishable goods (flowers, foods) –Goods that become obsolete (newspapers) –Services that are perishable (airline seats)

4. Example  Mean demand=3.85 How much would you order? Demand Probability 10.10 20.15 30.20 40.20 50.15 60.10 70.10 Total1.00

5. Single Period Inventory Control  Economics of the Situation Known: 1. Demand > Stock --> Underage (under stocking) Cost C u = Cost of foregone profit, loss of goodwill 2. Demand Overage (over stocking) Cost C o = Cost of excess inventory  C o = 10 and C u = 20 How much would you order? More than 3.85 or less than 3.85?

6. Incremental Analysis ProbabilityProbability Incremental Incrementalthat incrementalthat incremental Expected Demand Decisionunit is not neededunit is neededContribution 1First0.00 1.00-10(0.00)+20(1.00) =20 2Second0.10 0.90-10(0.10)+20(0.90) =17 3Third0.25 0.7512.5 4Fourth0.45 0.556.5 5Fifth0.65 0.350.5 6Sixth0.80 0.20-4 7Seventh0.90 0.10-7 C o = 10 and C u = 20

7. Generalization of the Incremental Analysis Chance Point Stock n-1 Decision Point Stock n Base Case nth unit needed nth unit not needed Pr{Demand  n} Pr{Demand  n-1} Cash Flow C u -C o 0

8. Generalization of the Incremental Analysis Chance Point Stock n-1 Decision Point Stock n Base Case Expected Cash Flow C u Pr{Demand  n} -C o Pr{Demand  n-1}

9. Generalization of the Incremental Analysis  Order the nth unit if C u Pr{Demand  n} - C o Pr{Demand  n-1} >= 0 or C u (1-Pr{Demand  n-1}) - C o Pr{Demand  n-1} >= 0 or C u - C u Pr{Demand  n-1} -C o Pr{Demand  n-1} >= 0 or Pr{Demand  n-1} =< C u /(C o +C u )  Then order n units, where n is the greatest number that satisfies the above inequality.

10. Incremental Analysis Incremental Demand Decision Pr{Demand  n-1} Order the unit? 1First0.00 YES 2Second0.10 YES 3Third0.25 YES 4Fourth0.45 YES 5Fifth0.65 YES 6Sixth0.80 NO- 7Seventh0.90 NO C u /(C o +C u )=20/(10+20)=0.66  Order quantity n should satisfy: P(Demand  n-1)  C u /(C o +C u )< P(Demand  n)

11. Order Quantity for Single Period, Normal Demand  Find the z*: z value such that F(z)= C u /(C o +C u )  Optimal order quantity is:  Do we order more or less than the mean if: –C u > C o ? –C u < C o ?

12. Example 1: Single Period Model  Our college basketball team is playing in a tournament game this weekend. Based on our past experience we sell on average 2,400 shirts with a standard deviation of 350. We make $10 on every shirt we sell at the game, but lose $5 on every shirt not sold. How many shirts should we make for the game?  C u = $10 and C o = $5; P ≤ $10 / ($10 + $5) =.667 Z.667 =.4 (from standard normal table or using NORMSINV() in Excel) therefore we need 2,400 +.4(350) = 2,540 shirts

13. Example 2: Finding C u and C o A textile company in UK orders coats from China. They buy a coat from 250€ and sell for 325€. If they cannot sell a coat in winter, they sell it at a discount price of 225€. When the demand is more than what they have in stock, they have an option of having emergency delivery of coats from Ireland, at a price of 290. The demand for winter has a normal distribution with mean 32,500 and std dev 6750.  How much should they order from China??